Those recent tweets have quickly become the most controversial messages posted during Trump's young presidency, and there have been increased calls for Twitter to disable the account in accordance with its rules.

For example, Twitter's policy says users "may not make threats of violence or promote violence" either directly or indirectly.

On Sunday, Trump tweeted a video that showed him slamming a person with a CNN logo superimposed over his face to the ground. One interpretation of that would be that Trump is showing his frustration with media outlets he thinks are critical of him. Another interpretation: It's OK to physically attack a journalist.

At best, the CNN tweet is an indirect promotion of violence. At worst, it's direct. Either way, it's a violation of Twitter's policy.

The policy also says users "may not incite or engage in the targeted abuse or harassment of others."

On Thursday, Trump tweeted that Brzezinski "was bleeding badly from a face-lift" when she visited his Florida estate late last year. In another tweet, he called her "dumb as a rock." That sounds a lot like harassment, whether you use the dictionary definition ("to create an unpleasant or hostile situation for especially by uninvited and unwelcome verbal or physical conduct"), the legal definition ("repeated conduct that is not wanted and is known to all parties as offensive"), or Twitter's guidelines.

A Twitter representative told CNN Sunday that it reviewed the CNN/WWE tweet and decided it did not violate its policy because there were many ways to interpret it and its "political context." That is true. There is a lot of political context in that tweet, not least because the president of the United States is spending his holiday weekend tweeting content inspired by an anonymous Reddit troll. (The same Reddit user has also posted a graphic depicting all the Jewish anchors on CNN, with a blue Star of David helpfully appended next to each face.)

For all the controversy provoked by Trump's tweets, there's no question that the POTUS's use of Twitter as his primary communication medium is good for Twitter. The microblogging service, whose business has been struggling for years, is enjoying its peak cultural relevance, thanks to the Tweeter in Chief.

But Twitter's harassment problem goes beyond what the president posts and is harmful to the interests of the company (and society) in the long run. And if it's serious about combatting abuse on its platform, Trump deserves to be held to the same standard as everyone else.

This column does not necessarily reflect the opinion of Business Insider.